Theorems · Definition · category theory

CategoryTheory.SingleFunctors.Hom.mk.noConfusion

{C : Type u_1} →
  {D : Type u_2} →
    {inst : CategoryTheory.Category.{v_1, u_1} C} →
      {inst_1 : CategoryTheory.Category.{v_2, u_2} D} →
        {A : Type u_5} →
          {inst_2 : AddMonoid A} →
            {inst_3 : CategoryTheory.HasShift D A} →
              {F G : CategoryTheory.SingleFunctors C D A} →
                {P : Sort u} →
                  {hom : (a : A) → F.functor a ⟶ G.functor a} →
                    {comm :
                        autoParam
                          (∀ (n a a' : A) (ha' : n + a = a'),
                            CategoryTheory.CategoryStruct.comp (F.shiftIso n a a' ha').hom (hom a) =
                              CategoryTheory.CategoryStruct.comp
                                (CategoryTheory.Functor.whiskerRight (hom a') (CategoryTheory.shiftFunctor D n))
                                (G.shiftIso n a a' ha').hom)
                          CategoryTheory.SingleFunctors.Hom.comm._autoParam} →
                      {hom' : (a : A) → F.functor a ⟶ G.functor a} →
                        {comm' :
                            autoParam
                              (∀ (n a a' : A) (ha' : n + a = a'),
                                CategoryTheory.CategoryStruct.comp (F.shiftIso n a a' ha').hom (hom' a) =
                                  CategoryTheory.CategoryStruct.comp
                                    (CategoryTheory.Functor.whiskerRight (hom' a') (CategoryTheory.shiftFunctor D n))
                                    (G.shiftIso n a a' ha').hom)
                              CategoryTheory.SingleFunctors.Hom.comm._autoParam} →
                          { hom := hom, comm := comm } = { hom := hom', comm := comm' } → (hom ≍ hom' → P) → P

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound